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Factorize 12x2 - 13x - 14

Mathematics

ScanSolve AI Answer

Answer

(4x - 7)(3x + 2)

Step-by-step solution

4 steps

Here's the step-by-step solution for factoring the quadratic expression 12x2−13x−1412x^2 - 13x - 14:

  1. Identify the coefficients and find two numbers that multiply to a×ca \times c and add to bb.

    For 12x2−13x−1412x^2 - 13x - 14, we have a=12a=12, b=−13b=-13, c=−14c=-14.
    We need two numbers that multiply to a×c=12×(−14)=−168a \times c = 12 \times (-14) = -168 and add up to b=−13b = -13. These numbers are 8 and −21-21.
    (8×−21=−1688 \times -21 = -168 and 8+(−21)=−138 + (-21) = -13)

  2. Rewrite the middle term using the two numbers found in Step 1.

    12x2+8x−21x−1412x^2 + 8x - 21x - 14
  3. Group the terms and factor out the greatest common factor (GCF) from each pair.

    4x(3x+2)−7(3x+2)4x(3x + 2) - 7(3x + 2)
  4. Factor out the common binomial factor.

    (4x−7)(3x+2)(4x - 7)(3x + 2)
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